The difference between the average of first ten prime numbers and the first ten prime numbers of two digits is:

First ten prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Sum of first ten prime numbers = $$2+3+5+7+11+13+17+19+23+29=129$$

Average of first ten prime numbers= $$\frac{129}{10}=12.9$$

Firtst ten prime numbers of two digits=11, 13, 17, 19, 23, 29, 31, 37, 41, 43

Sum of first ten prime numbers of two digits = $$11+13+17+19+23+29+31+37+41+43=264$$

Average of first ten prime numbers of two digits =$$\frac{264}{10}=26.4$$

Required difference = $$26.4 - 12.9 = 13.5$$